A drum contains forty liters of whisky. Four liters of whisky is taken out and replaced by soda. This process is carried out twice further. How much whisky is now contained by the container?

Suppose a solution contains x units of a whisky from which y units are taken out and replaced by soda

After n repeated operations, quantity of pure liquid remaining in solution

⇒ x(1 − y/x)ⁿ = x(1 − y/x)ⁿ units

Where n = number of replacements

So, whisky in the drum now:

⇒ 40 (1 − 4/40)³ = 40(1 − 1/10)³

⇒ 29.16

∴ 29.16 units of whisky is in the container

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